Abstract
Denote by script A sign(n) the family of isometry classes of compact n-dimensional Alexandrov spaces with curvature ≥ -1, and λk(M) the kth eigenvalue of the Laplacian on M ∈ script A sign(n). We prove the continuity of λk : script A sign(n) → R with respect to the Gromov-Hausdorff topology for each k, n ∈ N, and moreover that the spectral topology introduced by Kasue-Kumura [7], [8] coincides with the Gromov-Hausdorff topology on script A sign(n).
Original language | English |
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Pages (from-to) | x-15 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 53 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2001 Jan |
Externally published | Yes |
Keywords
- Alexandrov space
- Eigenvalue
- Laplacian
- Spectrum
- The Gromov-Hausdorff distance
- The spectral distance
ASJC Scopus subject areas
- Mathematics(all)